1. Field of Invention
The present invention relates to a switched capacitor circuit. More particularly, the present invention relates to the switched capacitor circuit having feedback compensation, an analog-to-digital converter and a compensation method.
2. Description of Related Art
FIG. 1 is a diagram illustrating a conventional switched capacitor circuit. Referring to FIG. 1, a non-inverting input terminal of a differential amplifier 110 is coupled to the ground. An inverting input terminal of the differential amplifier 110 is coupled to first terminals of capacitors CF and CS. The second terminal of the capacitor CF is coupled to an output terminal of the differential amplifier 110 or an input voltage Vin. The second terminal of the capacitor CS is coupled to the input voltage Vin or a reference voltage VREF. During a sampling period, switches SW12, SW13 and SW15 are closed, and switches SW11 and SW14 are open at the same time. Therefore, the input voltage Vin is charging the capacitors CF and CS. At the end of the sampling period, the switch SW15 is open. During an amplifying period, the switch SW14 is closed, the switch SW 13 are open, and the capacitor CS is connected to the reference voltage VREF. Meanwhile, the switch SW12 is open and the switch SW11 is closed so that the capacitor CF is connected to the output terminal of the differential amplifier 110.
If the differential amplifier 110 is ideal, that is, the gain of the differential amplifier 110 is infinite and the difference voltage VX between input terminals of the differential amplifier 110 is equal to 0, then the relationship between an output voltage VOUT, the input voltage Vin and the reference voltage VREF can be written as following equations (1) and (2) based on the law of charge conservation.Vin(CS+CF)=VREF×CS+VOUT×CF  (1)
                              V          OUT                =                                                            V                in                            ⁡                              (                                                      C                    S                                    +                                      C                    F                                                  )                                      -                                          V                REF                            ×                              C                S                                                          C            F                                              (        2        )            
If the capacitance CF and CS are the same, then as shown in the equation (2), the switched capacitor circuit in FIG. 1 is used to multiply the input voltage Vin by two and subtract the reference voltage VREF from the product. However, if the differential amplifier 110 is not ideal, then the gain (i.e. “A” hereinafter) is finite and the voltage VX is not equal to 0. In this case, the law of charge conservation can be written as a following equation (3), and the output voltage VOUT can be approximated as shown in a following equation (4).
                    {                                                                                                  V                    in                                    ⁡                                      (                                                                  C                        S                                            +                                              C                        F                                                              )                                                  =                                                                            (                                                                        V                          REF                                                -                                                  V                          X                                                                    )                                        ×                                          C                      S                                                        +                                                            (                                                                        V                          OUT                                                -                                                  V                          X                                                                    )                                        ×                                          C                      F                                                                                                                                                                                    -                                          V                      X                                                        ×                  A                                =                                  V                  OUT                                                                                        (        3        )            
                              V          OUT                ≈                                                                              V                  in                                ⁡                                  (                                                            C                      S                                        +                                          C                      F                                                        )                                            -                                                V                  REF                                ×                                  C                  S                                                                    C              F                                ×                      (                          1              -                                                1                  /                  A                                ⁢                                                                  ⁢                β                                      )                                              (        4        )                                β        =                              C            F                                              C              S                        +                          C              F                                                          (        5        )            
When 1/Aβ is small enough, the output voltage VOUT approximates to the ideal as disclosed in the equations (2) and (4). However, β is less than 1 as shown in the equation (5). Therefore, the gain A has to be large, and it becomes a design bottleneck and it is also an issue concerned by the people in the art.